On the Magnetic Field Configuration of the Magnetosheath

Terr. Atmos. Ocean. Sci., Vol. 24, No. 2, 265-272, April 2013 doi: 10.3319/TAO.2012.10.17.02(SEC)

Steven Michael Petrinec *

Lockheed Martin Advanced Technology Center, Palo Alto, California, USA

Received 16 April 2012, accepted 17 October 2012

Abstract

The magnetosheath is the region where the shocked solar wind interacts directly with the magnetosphere. Here we ex- amine the magnetic field throughout the equatorial magnetosheath as a function of the solar wind IMF direction using obser- vational data sets (Geotail and Wind) spanning 9.5 years. In general, the synoptic maps of the magnetosheath magnetic field are in agreement with the predictions of Rankine-Hugoniot conditions at the bow shock and with global numerical models. Qualitative comparisons with recent analytic magnetosheath magnetic field models are also performed and show that the compression of the magnetosheath magnetic field between the two boundaries (bow shock and magnetopause) used in such models is greater than that which is observed.

Key words: Magnetosheath, Bow shock, MHD discontinuities, Magnetopause Citation: Petrinec, S. M., 2013: On the magnetic field configuration of the magnetosheath. Terr. Atmos. Ocean. Sci., 24, 265-272, doi: 10.3319/TAO. 2012.10.17.02(SEC)

1. Introduction The interaction of the (shocked) solar wind and the magnetopause is the magnetosheath where the shocked so- Earth’s magnetic field has been the subject of considerable lar wind is slowed and diverted around the magnetopause. study since the 1960s (Spreiter et al. 1966; Fairfield 1967), The magnetic field of the magnetosheath is therefore after it was established through spacecraft observations that treated to zeroth order as a boundary value problem, such solar wind plasma is a consistent feature of interplanetary that the jump conditions across the bow shock are well-un- space (Gringauz et al. 1960; Neugebauer and Snyder 1962, derstood, and the boundary condition Bn = 0 at the magne- 1966). topause is understood. However, the region between these The solar wind has long been understood to behave as a two boundaries is not at all well-understood. This is due in collisionless magnetohydrodynamic (MHD) gas over large part to the difficulty in determining the locations and shapes spatial and lengthy time scales. The bow shock has been of these boundaries (e.g., the magnetopause is not a rigid recognized as a standing fast mode shock wave between the obstacle, but is self-consistent in pressure balance with the supermagnetosonic solar wind and magnetospheric obstacle. shocked solar wind, and the bow shock is located in a self- Thus, the change in plasma parameters and magnetic field consistent manner in relation to the magnetopause bound- across the bow shock follow Rankine-Hugoniot jump con- ary), and the effects of other plasma processes. Although ditions. It has also been long understood that the interaction it is understood that the magnetosheath magnetic field is between the shocked solar wind and the magnetosphere is tangent to the magnetopause, its orientation within the tan- characterized as a tangential discontinuity. At this boundary gential plane is not analytically understood. The orientation (the magnetopause), the shocked solar wind magnetic field at the magnetopause is extremely important because the is draped tangentially to the magnetopause surface (ignor- relation between the magnetosheath and magnetospheric ing for the moment non-ideal MHD processes such as mag- magnetic fields across the magnetopause is believed to de- netic reconnection). The region between the bow shock and termine where (and perhaps at what rate) magnetic reconnection occurs. Some recent statistical studies of the magnetosheath magnetic field have focused on the far downstream mag- * Corresponding author E-mail: [email protected] netosheath region (at X ~-30 RE using IMP-8 observations, 266 Steven Michael Petrinec

Kaymaz 1998), the low-latitude dawnside flank region ad- magnetosheath intervals, though it is noted that many of jacent to the magnetopause (using Equator-S observations, these intervals are quite brief as a result of boundary mo- Dunlop et al. 1999), and the draping configuration near the tions. There are three basic categories of magnetosheath magnetopause, Coleman (2005). In this study, we use the in intervals: (1) magnetopause to bow shock or bow shock to situ magnetic field observations from Geotail spacecraft to magnetopause (a sample crossing is shown in Fig. 1); (2) produce synoptic maps of the equatorial magnetosheath re- bow shock to bow shock (Fig. 2); and (3) magnetopause to gion field intensity and orientation within the plane for vari- magnetopause (Fig. 3). ous interplanetary magnetic field (IMF) orientations. Quali- The magnetosheath intervals were then matched with tative comparisons with analytic models are also performed. convected solar wind observations from the Wind spacecraft (Lepping et al. 1995; Ogilvie et al. 1995). Solar wind and magnetosheath parameters have been averaged down to 2. Empirical results a 5-minute resolution. The choice of this time resolution was The observations used in this study of the magne- based on several factors. First, the Wind plasma moment tosheath magnetic field are from the Geotail spacecraft parameters at higher resolution (several tens of seconds) (Kokubun et al. 1994). The Geotail orbit is at low inclina- are not provided at uniform cadence. Second, it is believed tion; thus, this study is focused on the magnetosheath in the that a higher time resolution does not improve the analyses, equatorial region. The magnetosheath intervals have been since the neighboring samples in time are less likely to be identified by direct observation by the author, high-school statistically independent. Last, the convection time from the students and teachers hired for the summer through the In- solar wind monitor to the magnetosheath-sampling space- dustry Initiatives for Science and Math Education program craft is not known to be better than a few minutes especially (IISME). Bow shock crossings are readily identified as sud- since the plasma velocity is slowed after crossing the bow den changes in the ion moments and magnetic field intensity shock. which are not present in the solar wind in accordance with The convection time was taken as Δx/Vsw up to the ll that expected from Rankine-Hugoniot relations. The mag- bow shock, with an additional DDtx= //Vsw 3 for those netopause crossings are best identified as a change in the locations within the magnetosheath. The aberration angle magnetic field clock angle from that which varies in close of the solar wind at each instance was used to adjust the agreement with the IMF clock angle to that which is steady magnetosheath locations into an aberrated Geocentric Solar and independent of the IMF clock angle. The magnetosheath Ecliptic (GSE) coordinate system. intervals span the period from April 1996 through October The magnetosheath intervals occur during various so- 2005. This extended time span resulted in 6175 separate lar wind conditions; therefore, the boundaries during these

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Fig. 1. An example of a magnetosheath interval, as the Geotail spacecraft crosses from the solar wind to the magnetosphere (blue traces). (a) Ion density. (b) Magnetic field intensity. (c) IMF clock angle. The convected Wind observations (black traces) are included for solar wind context. Magnetic Field Configuration of the Magnetosheath 267 times are crossed at various distances. To produce synoptic the Shue et al. (1998) magnetopause model for a solar wind maps of the magnetic field, the next step was to normal- dynamic pressure of 2 nPa and zero IMF Bz. The normaliza- ize the magnetosheath passes to common inner and outer tion process scales many of the magnetosheath passes such boundaries by using empirical models as parameterized by that they begin and end at the empirical model boundaries. the solar wind condition. The models used in this study are However, due to boundary oscillations and other dynamics the Farris and Russell (1994) model for the bow shock and and uncertainties, many of the normalized passes do not ‘fit’

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Fig. 2. A sample Geotail magnetosheath interval, bounded on both sides by the bow shock. The format is the same as Fig. 1.

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Fig. 3. A sample Geotail magnetosheath interval bounded on both sides by the magnetopause. The format is the same as Fig. 1. 268 Steven Michael Petrinec between the boundaries. Therefore, a second normalization which the absolute value of the z-component of the IMF process has been used to force the ends of each pass to match is small compared with the root-mean-square of the x- and 2212 the magnetosheath boundaries. Specifically, if the portion y- components BBzx< + B2y . Figure 4a shows a 7 ^hA of a pass which has been identified as ‘magnetosheath’ has contour plot produced from the median values of the inten- end points which do not match the model boundaries (after sity of the magnetosheath magnetic field normalized by the normalizing by the solar wind parameters), then the spatial intensity of the IMF BBTT-IMF , at 0.5 × 0.5 RE spatial reso- ^h locations relating to the pass are linearly scaled (typically lution. The magnetic field intensity ratio near the subsolar by a few percent at most) such that the endpoints do match bow shock is greater than three which is expected from the the boundaries. Rankine-Hugoniot relations. Figure 4b shows the median The 5-minute samples of the magnetosheath magnetic magnetic field vector orientation within this plane in 1 × field were then filtered by the orientation of the IMF and 1 RE bins (blue line segments). The resulting vector direc- collected into Cartesian bins according to the aberrated and tions are also as expected; the vector field smoothly varies normalized location of the spacecraft. For those bins within throughout the magnetosheath, and is not significantly dif- which there were at least 6 samples; the median magnetic ferent between dawn and dusk. The contour levels of the field strength (normalized by the IMF intensity) and the intensity ratio are also similar between dawn and dusk. To median magnetic field orientation are determined. Medians present this more explicitly, the median intensity as a func- values are used so that any dynamics or errors in the esti- tion of XaGSE along the dawn and dusk directions are shown mated solar wind convection time which produce outliers in Fig. 5. These values are calculated in 15 angular bins from do not significantly skew the determination of the ‘typical’ an origin located just inside of the subsolar magnetopause magnetic field. (9 RE). The XaGSE ranges (horizontal bars) in Fig. 5 are de- In Fig. 4, synoptic maps of the aberrated GSE equato- termined from the intersection of the angular bins with the rial plane are created for the cases when the IMF is within magnetosheath region. Markers are placed at the center of

20° of the normal to the solar wind flow direction and for the XaGSE range. The vertical error bars display the first and

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Fig. 4. All Geotail magnetic field observations of the equatorial magnetosheath, when the IMF is within 20° of perpendicular to the solar wind flow direction and for small IMFBz . Contour plot of the normalized magnetic field intensity (a) and orientation of the magnetosheath magnetic field (b). Magnetic Field Configuration of the Magnetosheath 269 third quartiles of the magnetic field intensity ratio. As can Figure 6 is similar to Fig. 4, but is filtered to those be seen, the dawn and dusk magnetosheath field ratios are samples for which the IMF lies within 10° of the nominal approximately equal, as expected for IMF conditions which Parker-Spiral angle (i.e., ~-45°/135° from the Sun-Earth have large By - component compared to either the X- or Z- line). In this case, the magnetic field intensity ratio contours components. (left) are larger in the duskside than in the dawnside dayside

Fig. 5. Median magnetic field increase in the magnetosheath along dawn and along dusk, as a function of X-distance. Vertical error bars denote the first and third quartile values.

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Fig. 6. The same format as Fig. 4, but for IMF intervals which lie close to the Parker-spiral angle direction. 270 Steven Michael Petrinec magnetosheath. Near the dayside bow shock surface, the 90°, and slowly decreases with increasing distance down- variation of the magnetic field ratio is again as expected from tail as the magnetic field drapes around the magnetopause Rankine-Hugoniot relations (Petrinec and Russell 1997). obstacle. The x-ranges in Fig. 8 are the same as is used in The right side of Fig. 6 again shows the median orien- Fig. 5. The vertical error bars represent the first and third tation directions of the equatorial components of the magne- quartiles of the field deviation angle within each bin. It is tosheath magnetic field. The chaotic nature of the magnetic seen that the median deviation angle varies smoothly with field directions in the dawn side magnetosheath region is distance down the dusk magnetosheath flank. The different consistent with previous studies of the dynamics and shock IMF conditions cause the deviation (draping) angle to vary reformation processes associated with the quasi-parallel at different rates along the duskside magnetosheath. bow shock. On the dusk side magnetosheath, the orientation Last, a quick comparison of the magnetic field inten- vectors are much more ordered. sity ratios is made between the observations and recent ana-

In Fig. 7, the IMF orientation atan (By/Bx) is limited lytic models. Two analytic magnetic field models describ- to angles within the equatorial plane between -10° and -30° ing the magnetosheath have been put forth by Kobel and from the radial flow direction, towards the direction of the Flückiger (1994) and by Romashets et al. (2008). The Kobel Parker-Spiral direction (at ~-45°/135°). Similar to Fig. 6, and Flückiger model determines a magnetic scalar potential the magnetic field intensity ratio is larger in the dusk than within a region bounded by two paraboloids representing the dawn dayside magnetosheath region; as expected, the the magnetopause and bow shock. The scalar potential is median magnetic field vectors are better aligned in the dusk expressed in terms of the IMF, and the magnetosheath mag- than the dawn magnetosheath. netic field is then determined from the scalar potential. The Figure 8 shows the median magnetosheath magnetic Romashets et al. (2008) model uses the same boundaries, field deviation angle from the X-axis along the dusk mag- but solves for the magnetic vector potential, thus allowing netosheath, for the three IMF cases shown in Figs. 4, 6, and for a non-zero distributed current density within the mag- 7. In the dayside region, the deviation angle is closest to netosheath.

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Fig. 7. The same format as Fig. 4, but for IMF intervals which lie between the solar wind flow direction and the Parker-spiral angle direction. Magnetic Field Configuration of the Magnetosheath 271

In Fig. 9, we plot the magnetic intensity ratio within analytic models. In particular, the magnetic field intensity the magnetosheath region of both analytic models for a ratios on the dusk side flanks are significantly higher in the Parker-spiral IMF configuration. The resulting maps from analytic models than in the observations, and are higher the two models are very similar, with higher field strength than expected from the Rankine-Hugoniot relations across in the subsolar region and along the dusk flank than in the the dusk side bow shock. It is suggested that the reason for dawn flank region. A qualitative comparison between these the discrepancy is that the use of paraboloid shapes for both results and those shown in Fig. 6a illustrates that there are boundaries in the analytic models allows too little room for considerable differences between the observations and the the magnetic flux tubes to pass around the obstacle in the

Fig. 8. The median angle of magnetic field draping (with respect to the X-axis) along the dusk magnetosheath, as a function of distance along the X-axis. The three traces represent the IMF cases shown in Figs. 4 (red), 6 (blue), and 7 (black). Horizontal bars represent the range of XaGSE in the magnetosheath bin. Vertical error bars represent the first and third quartiles.

Fig. 9. Magnetic field intensity ratio maps for two analytic magnetic field models, for the Parker-spiral angle IMF configuration. 272 Steven Michael Petrinec same way as in nature, and that different boundary shapes gas, energetic electrons, and corpuscular solar emis- need to be considered. sion, using three-electrode charged-particle traps set up on the second Soviet cosmic rocket Luna 2. Dokl. Akad. Nauk USSR, 131, 1301-1304. 3. Conclusions Kaymaz, Z., 1998: IMP 8 magnetosheath field compari- The large-scale structure of the magnetosheath mag- sons with models. Ann. Geophys., 16, 376-387, doi: netic field intensity and orientation as observed by the 10.1007/s00585-998-0376-3. [Link] Geotail spacecraft is in accordance with the general knowl- Kobel, E. and E. O. Flückiger, 1994: A model of the steady edge of expected behavior. The jump in the magnetic field state magnetic field in the magnetosheath. J. Geophys. intensity across the bow shock is in good agreement with Res., 99, 23617-23622, doi: 10.1029/94JA01778. [Link] Rankine-Hugoniot relations. Also, the magnetic field in the Kokubun, S., T. Yamamoto, M. H. Acuña, K. Hayashi, region downstream of the quasi-parallel bow shock is more K. Shiokawa, and H. Kawano, 1994: The GEOTAIL disordered than downstream of the quasi-perpendicular bow magnetic field experiment. J. Geomagn. Geoelectr., shock. Finally, it is recognized from a qualitative compari- 46, 7-21. son of the observations with analytic models that more work Lepping, R. P., M. H. Acũna, L. F. Burlaga, W. M. Farrell, J. needs to be done to improve the analytic magnetosheath A. Slavin, K. H. Schatten, F. Mariani, N. F. Ness, F. M. models. Specifically, it is believed that the use of boundary Neubauer, Y. C. Whang, J. B. Byrnes, R. S. Kennon, shapes which allow for greater magnetosheath thickness in P. V. Panetta, J. Scheifele, E. M. Worley, 1995: The the flank regions will result in more favorable comparisons Wind magnetic field investigation. Space Sci. Rev., 71, of the flank magnetosheath magnetic field intensity between 207-229, doi: 10.1007/BF00751330. [Link] analytic models and observations. Neugebauer, M. and C. W. Snyder, 1962: The mission of Mariner 2: Preliminary observations, solar plasma ex- Acknowledgements The author wishes to thank the Geo- periment. Science, 138, 1095-1097. tail and Wind instrument and science teams for providing Neugebauer, M. and C. W. Snyder, 1966: Mariner 2 ob- the observations to the public via CDAWeb. In addition, the servations of the solar wind: 1. Average properties. J. author thanks Elle Allen, Katy Kuei, Marcos Pedreiro, and Geophys. Res., 71, 4469-4484, doi: 10.1029/JZ071i01 Janine Stovall for their efforts and contributions in identi- 9p04469. [Link] fying geophysical boundaries in the Geotail data sets. This Ogilvie, K. W., D. J. Chornay, R. J. Fritzenreiter, F. 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